Two dimensional advective heat flux estimation from velocity measurements

The advective heat flux, ρc_pv · ∇T, is an important quantity in edge flames because the sign of v · ∇T characterizes relative propagation direction of the edge flame, and its magnitude gives information regarding strength of the resulting propagation or extinction front. Modern laser techniques can measure the velocity and temperature fields simultaneously within a flame, but accurate measurements of temperature simultaneous with velocity outside the high temperature region of the flame are more difficult and time-resolved measurements of velocity and temperature simultaneously for unsteady flows require complex measurement systems. In this paper, the theoretical framework to show that the flow dilatation can be used to directly estimate a scaled advective heat flux is presented. Numerical simulations of both a positive (propagating) and negative (extinguishing) edge flame were studied to assess the relationship between dilatation and advective heat flux. Experimental measurements of the two-dimensional component of dilatation in positive and negative edge flames were also made and compared to the simulations. The full advective heat flux was well represented by the dilatation in the simulations, and the experimental data demonstrates that the measured dilatation is useful for estimating advective heat flux. Flames with varying positive and negative flame speeds are examined with the technique.